Answer
$2\sqrt{17}$ units.
Work Step by Step
RECALL:
The distance $d$ between the points $(x_1, y_1)$ and $(x_2, y_2)$ can be found using the distance formula:
$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$
Use the formula above to obtain:
$d=\sqrt{(3-5)^2+(-4-4)^2}
\\d=\sqrt{(-2)^2+(-8)^2}
\\d=\sqrt{4+64}
\\d=\sqrt{68}
\\d=\sqrt{4(17)}
\\d=\sqrt{2^2(17)}
\\d=2\sqrt{17}$
Thus, the distance between the two given points is $2\sqrt{17}$ units.